FOR CUSTOMER LIFETIME V E-COMMERCE...segmenting data by marketing channels, we would extremely need...

The 8th

International Days of Statistics and Economics, Prague, September 11-13, 2014

528

MANAGERIAL IMPACTS OF DIFFERENT COMPUTATION MODELS

FOR CUSTOMER LIFETIME VALUE FOR AN E-COMMERCE

COMPANY

Pavel Jašek – Lenka Vraná

Abstract

Long-term profitability of a customer is a really important subject for commercial

organizations. The concept of Customer Lifetime Value helps companies to manage their

acquisition and retention marketing activities based on appropriately discounted net

contribution margin achieved per customer.

There are six main approaches for Customer Lifetime Value Modeling which are

based on advanced statistical, econometric and data mining algorithms. Authors describe

profoundly three of these approaches (Recency, Frequency and Monetary Value models,

probability models and persistence models) on theoretical basis and compare their results on

real-world data from an online fashion retailer.

Managerial implications of usage of different models are discussed. Companies need

to decide what business goals are they trying to achieve with CLV analysis and predictions.

Main decisions should be made on a level of detail (individual vs. aggregate) and a predicted

variable (number of transactions, customer value or probability of being alive only). The

article concludes specific use cases for various models: RFM serves great as an introductory

tool to customer segmentation, Pareto/Negative Binominal Distribution predicts customer’s

probability of being alive and Vector Autoregressive Model interprets various relationships

among customer acquisition metrics.

Key words: Customer Lifetime Value, Pareto/Negative Binominal Distribution,

Econometrics Modeling

JEL Code: M21, C52, M31

Introduction

Customer Lifetime Value (CLV) is defined as the net present value of all the profits that a

specific customer brings to the firm (Berger & Nasr, 1998). It can serve as an indicator of

profitable individuals. Customer Equity (CE) is then sum of CLV of all the current and the

future customers and can therefore serve as a tool how to measure the firm’s performance.

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(Gupta, Hanssens, Hardie, & Kahn, 2006) classify the CLV (or CE) modeling

techniques into six branches: 1) recency, frequency, monetary value (RFM) models predict

behavior of the customers in the next time period only, 2) probability models use probability

distributions and their combinations (e.g., Pareto/NBD) to predict whether the customer will

still be active in the future and if so, how will he act, 3) econometrics models combine models

of customer acquisition, retention and expansion to estimate CLV, 4) persistence models also

work with these elements, but treat them as a dynamic system and use methods of

multivariate time series analysis, 5) computer science models consist of various data mining

and machine learning algorithms and 6) diffusion/growth models focus on predicting customer

equity.

We select three of these approaches (RFM models, probability models and persistence

models), describe them in detail and compare their results.

1 Comparison of CLV Models Computations

Although we work only with three types of the algorithms described above, the comparison is

very difficult. The RFM and probability models use detail data about customers and can

predict CLV for each individual as well as CE. Persistence models analyze aggregated data

and therefore can be used only to forecast CE. This leads to different managerial use cases.

We had to define metrics, which would enable us to evaluate the results, similarly to

(Wübben & von Wangenheim, 2008). We decided to divide the dataset into two pairs of

training and validation data. We divide the dataset into 50/50 and 90/10 time periods in order

to compare long-term prediction based on short history and short-term prediction based on

long history. We use the trained models to score one particular customer (for CLV estimation)

and the whole customer set (to predict CE). Chapter 5 contains the actual comparison of the

estimated and actual values.

1.1 Dataset Description

For the purpose of this article we have used real-world data from a Czech online retailer

pseudo named MP. The business sells fashion primarily to mid-aged women and regularly

twice a year changes a large portion of product catalogue in order to match summer and

winter season. According to the customer base classification done by (Fader & Hardie, 2009,

p. 63), this dataset has non-contractual relationship with customers and continuous

opportunities for transactions.

This historical log contains 77 289 logged-in visits to the e-commerce website and

33 613 online purchases made by 29 589 different customers from the time period

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of September 1, 2011 to March 31, 2014 (134 weeks in total). Cut-off dates for 50/50 model

validation would be December 15, 2012 and for short validation December 31, 2013.

Thoroughly in this article we would illustrate some calculations using one selected

customer called Alice. Data sample in Table 1 gives a preview of sales data for such

customer. In total Alice had 17 transactions of total revenue 14 162 CZK, dating from

November 17, 2011 to December 12, 2013. In comparison with the average of 1.74

transactions and 2 086 CZK average sum of revenues per active customer it is evident Alice is

an outlier, yet her example still serves great for explanative purposes.

Tab. 1: Dataset sample for Customer #22862 (Alice)

Row ID Customer # Date Sales (CZK)

2712 22862 2011-11-17 1 540

3336 22862 2011-11-26 434

9257 22862 2012-05-05 1 120

9550 22862 2012-05-11 273

Source: Sample dataset for online retailer MP.

Unfortunately, the dataset does not include any cost data related to marketing expenses. One

of ordinary assumptions for CLV modeling is its focus on profit and not only revenue. For the

purposes of this article we will be consciously breaking this rule relying only on revenue

metrics as we’re not comparing different models of profitability computation. Once we started

segmenting data by marketing channels, we would extremely need cost data in order to

deliver valid results.

2 RFM Modeling

RFM analysis is a marketing technique used for analyzing customer behavior such as how

recently a customer has purchased (recency), how often the customer purchases (frequency),

and how much the customer spends (monetary), as defined in (Bult & Wansbeek, 1995).

Traditionally, this discretization relies on quintiles. Implementation of RFM analysis

done by (Han, 2013) discretized recency according to expected purchasing cycle, frequency

according to number of purchases and monetary according to value intervals. Han followed

this discretization by building and visualization of generalized linear model of quasibinominal

family with logit link that we’ve used in this article as well. The graphical and statistical

output can be seen in Figure 1 and Table 2, respectively.

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Fig. 1: Scatter plot of RFM components for Probability of Purchasing

Source: calculated by the authors using R software and (Han, 2013) R script based on sample data.

Visualization provided in Figure 1 serves well for managerial discussions. The scatter plot

suggests that there is an obvious linear or exponential fall relationship between the repurchase

percentage and the Recency, and an obvious exponential rise relationship between the

repurchasing percentage and the Frequency. However, there is no obvious relationship

between the repurchasing percentage and the Monetary. Such results are completely aligned

with CDNOW dataset examined by (Han, 2013).

Tab. 2: RFM Model estimated parameters for the sample dataset

Coefficient Estimate Standard Error

Intercept -1.6768 0.0647 ***

Recency -0.1500 0.0107 ***

Frequency 0.5915 0.0247 ***

Monetary Value 0.0009 0.0003 ***

Source: calculated by the authors using R software based on sample data. *** Significant at 1% level.

Quasibinomal logit model for Buy ~ Recency + Frequency + Monetary.

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Estimated coefficients for parameters in Table 2 indicates that historical purchases don’t

matter that much, but in contrary recent purchases and moreover the number of purchases is a

really strong predictor of purchase behavior.

RFM Model in Table 2 can be used for individual predictions based on customer

purchase information. In the 50/50 training data set, Alice made her last purchase on

November 24, 2012, thus her Recency bucket is 0, Frequency is 7 transactions and Monetary

value is 92 due to 10 CZK discretization. Predicted probability of Alice’s repurchasing is

93.03 %. Expected CLV for validation period for Alice given 2 % discount rate is

580.87 CZK.

3 Probability Models

Pareto/NBD model implementation by (Fader, Hardie, & Lee, 2005) simplifies original

Schmittlein’s computation. This model serves for repeat-buying behavior in a non-contractual

setting and is based on assumptions that the number of transactions made by a customer

follows a Poisson process with transaction rate λ and that heterogeneities in transaction and

dropout rates across customers follow a gamma distribution with shape parameters r and s,

respectively, and scale parameters α and β, respectively.

Application in this article was inspired by 1) (Wadsworth, 2012) in his implementation

of R’s package BTYD (Buy 'Til You Die) by (Dziurzynski & Wadsworth, 2012), 2) (Baggott,

2013) and 3) package BTYD_plus that extend the basic package (Platzer, 2008).

Results of Pareto/NBD model calibration for sample dataset are shown in Table 3 and

discussed below.

Tab. 3: Pareto/NBD Model estimated parameters for the sample dataset

Pareto/NBD model

parameters

r α r/α s β s/β Log-

Likelihood

Weekly aggregation,

50/50 training

0.5699 33.4427 0.0170 0.2868 7.7247 0.0371 -27594.94

Weekly aggregation,

90/10 training

0.5446 39.0630 0.0139 0.4244 19.9702 0.0212 -62074.56

Source: calculated by the authors using R software based on sample data.

According to the interpretation of Pareto/NBD parameters described by (Wübben & von

Wangenheim, 2008), r/α represents the number of purchases of an average customer in one

time unit. In our dataset an average customer makes 0.02 transactions per week. The lifetime

of an average customer is exponentially distributed with parameter s/β and has an expected

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value of 1/(s/β), where s/β represents the dropout rate of an average customer per time unit.

An average customer remains active for 27 weeks, or 189 days respectively.

1

1)1(

,,,|)(

s

ts

rsrtXE

(1)

Formula 1 proposed by (Fader, Hardie, & Lee, 2005) computes the expected number of repeat

transactions in a period of length t for a random customer. For 52-week long period, this

metric is 0.61. For Alice, expected number of transactions conditional on her past behavior

(e.g. frequency 6 transactions, time of last interaction 53.29 weeks, 56.29 total time observed)

is 3.42 in the same 52-week long period.

Fig. 2: Distribution of customers by probability of being alive

Source: calculated by the authors using R software based on sample data and script by (Baggott, 2013).

Figure 2 shows very positive results for the company: the majority of current customer base

has probability of being alive higher than 0.5. Yet as we would see in Figure 3, the predictive

ability is not ideal.

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Fig. 3: Comparison of transactions by repeat buyers in Pareto/NBD model

Source: calculated by the authors using R software based on sample data of 13 661 transactions and 50/50

training/validation set. Transactions from customers with 1 purchase only were removed.

Figure 3 shows the output of Pareto/NBD model with actual number of transactions. It is

visually understandable that overall performance of the model is good, yet it underestimates

weekly deviations.

(Fader, Hardie, & Lee, 2005) also mention that a weakness of Pareto/NBD is its

possibility of predicting number of transactions only.

4 Persistence Models

In 2008 Villanueva et al. described application of vector autoregressive model (VAR) to

customer equity predictions. They researched impacts of customer acquisition on the

company’s performance. They examined the differences between customers gained by

marketing activities and customers acquired spontaneously.

The model is designed as the classical VAR(p) model, where p stands for the number

of lags. It captures dynamic relationships between three time series: number of customers

acquired by marketing actions (MKT), number of customers acquired by word of mouth

(WOM) and the firm’s performance (VALUE):

1 11, 12, 13, 1,

2 21, 22, 23, 2,

1

3 31, 32, 33, 3,

t l l l t l tp

t l l l t l t

l

t l l l t l t

MKT c a a a MKT e

WOM c a a a WOM e

VALUE c a a a VALUE e

, (2)

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where t stands for time, vector (c1, c2, c3)’ contains the constant terms and vector (e1,t, e2,t,

e3,t)’ contains the error terms with Gaussian white noise properties. Model in this form can

describe the following relationships (Villanueva, Yoo, & Hanssens, 2008):

- direct effects of acquisition on the firm’s performance (coefficients a31,l and a32,l),

- cross-effects between two types of customer acquisition (coefficients a12,l and a21,l),

- feedback effects, which states how the firm’s performance affects the acquisition in the

next time periods (coefficients a13,l and a23,l),

- reinforcement effects, when value of series in time t affects its future values, e. g.

customers acquired by word of mouth would spread the positive information about the

firm which would lead to more acquisitions (coefficients a11,l, a22,l and a33,l).

Villanueva et al. discovered that customers gained by marketing promotions generate higher

value in short term. However, customers acquired spontaneously had greater impact in long-

term evaluation. We try to apply their approach on online retailer data and compare the

results.

As we are missing more detailed data, we define newly acquired customers in time t as

customers, who make their first purchase. Therefore we use first year data as a purchase

history and we don’t include them in the analysis. We work with weekly time series from

September 1, 2012 to December 31, 2013. We keep 2014 data as the validation set.

We add data from Google Analytics to distinguish between MKT and WOM

customers. Villanueva et al. used number of log-ins as VALUE series as they were working

with data from internet firm that provided Web hosting. We tried to use income as firm’s

performance indicator, but there was no significant dependency of income on number of

acquired customers, so we used number of purchases. Because the new customer is not

identified until he makes her first purchase, the analysis focuses on any subsequent purchases.

All the series are tested for unit root by augmented Dickey-Fuller test and KPSS test

and are recognized as stationary (their means and variances are time invariant). To minimize

the Akaike information criterion we fitted VAR(1) model:

1

1

1

68.51 0.92 0.00 0.27

40.82 0.75 0.59 0.32

237.96 2.60 0.00 0.80

t t

t t

t t

MKT MKT

WOM WOM

VALUE VALUE

. (3)

The coefficients a12 and a32 are insignificant and are set to zero, thus there is no direct effect

of WOM customers on firm’s performance and no cross effect of WOM customers on MKT

acquisitions.

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The actual number of purchases made during the validation period (from January 1,

2014 to March 31, 2014) is equal to 2 781. The model predicts 2 881 purchases in the

corresponding period, however the predictions quickly revert to the mean.

Based on the fitted model we also create impulse response functions (Figure 4), that

show the response of VALUE series to newly acquired customer via marketing promotion or

word of mouth. The effect includes not only purchases made by the new customer, but also

purchase activity of others which could have been encouraged by the newcomer (Villanueva

et al., 2008).

Fig. 4: Direct effects of customer acquired through marketing promotions (MKT) and

customer acquired spontaneously (WOM) on number of purchases (VALUE)

Source: calculated by the authors using R software based on sample data.

As the model doesn’t find any direct effects of WOM on firm’s VALUE, the impulse response

function (weekly effects as well as accumulated) is constant and equal to zero. This means

that the WOM customers usually make only one purchase (the one when they are identified as

new customers) and no more. This zero effect of WOM is in contrast with the study done by

(Smutný, Řezníček, & Pavlíček, 2013), where customers of a studied telecommunications

company influenced their own interactions more than communications activities of the studied

brand itself, thus impacting positively WOM channels.

The function of weekly effects shows that each unexpected acquisition made through

the marketing channel generates 2.60 additional purchases during the first week and then the

effect fades. The new MKT customer causes 3.14 additional purchases during her whole

lifetime.

For the case of Alice, who is customer gained by the marketing activity, VAR model expects

her to generate 4.14 purchases during her whole lifetime. This value underestimates the actual

number as Alice is an outlier customer.

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The results of our analysis are opposite to the results of Villanueva et al. Their company’s

value is affected mostly by WOM customers; our model suggests that the WOM customers

don’t have any significant impact on the firm’s performance after their first purchase.

5 Discussion and Managerial Impacts

As mentioned in chapter 1, the comparison is not easy. In this article we researched three

different types of models that can be used in CLV computations, but each of them yields

diverse results and is based on inconsistent assumptions even though sharing many e.g.

convenience in non-contractual settings.

5.1 Model Comparison

Primary implementations of models used in this article could not compete with entire

comparisons of stochastic models in the paper of (Wübben & von Wangenheim, 2008), in

which many important metrics were proposed. Table 4 shows some of comparable results.

Pareto/NBD results for number of transactions is significantly lower than actual data.

Meanwhile, VAR model’s estimation of 2 881 transactions in validation period compared

with 2 781 transactions in actual data is a great result (moreover, counting aggregate-level

only).

Tab. 4: Comparison of CLV computation models

Statistic for validation period Actual data RFM Pareto/NBD VAR

Transactions in 50/50 test method 8 180 N/A 7 137 N/A

Transactions in 90/10 test method 2 781 N/A 1 742 2 881

Transactions for Alice in 50/50 test method 10 N/A 0.18 N/A

Purchase value for Alice in 50/50 test method 7 749 5 809 N/A N/A

Transactions for Alice in 90/10 test method 0 345 N/A N/A

Source: calculated by the authors using R software based on sample data. VAR model training period started on

September 1, 2012.

Pareto/NBD implementations used in this article understood Recency as a difference of last

and first transaction date. In contrary, RFM Model captures Recency as the difference

between the studied end date and last transaction date.

5.2 Discussion on Managerial Implications

From such incomparable results it is noticeable that the company needs to decide what

business goals it is trying to achieve with CLV analysis and predictions. Main questions

should lead to decision on level of detail (individual vs. aggregate) and predicted variable

(number of transactions, customer value or probability of being alive only).

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Each model serves its purpose and can be adapted for specific business goals. RFM

Model exhibited clear visual explanation of its factor strength, Pareto/NBD worked well with

probabilities of customers being alive and vector autoregressive model indicated possible

relations between variables and various time shifts.

RFM Model demonstrated the prediction strength of Recency and Frequency and

prediction weakness of Monetary value. High-value historical purchases doesn’t implicate

future transactions.

On the other hand, high probability of repurchasing by very recent customers with

high number of transactions can lead to managerial decisions of increased marketing activities

on this segment of customers. For future research, additional information about marketing

activities should be incorporated.

According to (Wübben & von Wangenheim, 2008) the performance of heuristic

estimation of customer value and segmentation can be as good as stochastic models. The

paper also states that one third of top 20 customers gets predicted badly. Managerial

implications are very clear – another customers should deserve being part of top 20 privileges,

but the model does not nominate them. Such customers could spread negative feedback about

the company.

Another criticism mentioned by Wübben et al. is the reliability of customer-centric

models when training and predictions results only for several transactions in long time period

only.

VAR models in CLV analyses can characterize behavior of the average customer

gained by marketing campaigns or by word of mouth. In case of online retailer, we find out

that WOM customers aren’t loyal and that they don’t affect the performance of the firm after

their first purchase. On the other hand, customers acquired by marketing promotion generate

4.14 purchases during their whole lifetime.

VAR models use aggregated data and do not allow analysis of data with finer

granularity. They could be used to forecast the future firm performance, but the predictions

(in our case) are quickly reverting to the mean and don’t capture the actual fluctuations well.

The advantage of VAR models is their scalability: different indicators can be used as

VALUE series and therefore we can examine different sets of relationships. One of the

possible extensions could be to include more than one MKT series to assess the impacts of

several marketing campaigns. The multivariate time series analysis is well described topic

nowadays and so the possibilities of its application are wide.

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Conclusion

This paper presented three main approaches to computations used in CLV analysis and

modeling. RFM, Pareto/NBD and VAR models were compared on real-world data from an

online fashion retailer based in the Czech Republic. Extensive dataset helped with apt

visualizations of model results and plenty of validation possibilities.

During the research, many important questions and possible research extensions arose.

Estimation of profit data in case of Pareto/NBD and VAR models and transactions in case of

RFM predictions are two of the main fragilities of such modeling.

Various managerial impacts were discussed. RFM served great as an introductory tool

to customer segmentation, Pareto/NBD predicted customer’s probability of being alive and

VAR model interpreted various relationships among metrics.

Acknowledgement

This paper was written with the financial support of IGA grant F4/18/2014.

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Contact

Ing. Pavel Jašek

University of Economics, Prague

W. Churchill Sq. 4, Prague 3, Czech Republic

[email protected]

Ing. Lenka Vraná

University of Economics, Prague

W. Churchill Sq. 4, Prague 3, Czech Republic

[email protected]

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